Of Motion: An Elementary Treatise |
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Page xi
... circle through the highest or lowest point 75 135 . 137 . Two cases of motion on inclined planes of bodies connected with strings ib . General case of motion on a smooth plane curve 77 140 . Motion on a cycloid 79 142 . Oscillations in ...
... circle through the highest or lowest point 75 135 . 137 . Two cases of motion on inclined planes of bodies connected with strings ib . General case of motion on a smooth plane curve 77 140 . Motion on a cycloid 79 142 . Oscillations in ...
Page 75
... circle through the highest or lowest points are the same . Let A be the lowest point of a circle , and let t be the time of descent down any chord AC . Also let AB be the diameter , and the angle BAC = 0 . Then the force down AC is W ...
... circle through the highest or lowest points are the same . Let A be the lowest point of a circle , and let t be the time of descent down any chord AC . Also let AB be the diameter , and the angle BAC = 0 . Then the force down AC is W ...
Page 79
... circle , whose di- ameter RT is vertical and = 2a . R T A Then PT is a tangent to the cycloid ( Appendix , Art . 2 ) . The acceleration on the particle in the direction of its motion = g cos PTR = g PT ᎡᎢ = 9 AP 2 ᎡᎢ ( App . Art . 3 ) ...
... circle , whose di- ameter RT is vertical and = 2a . R T A Then PT is a tangent to the cycloid ( Appendix , Art . 2 ) . The acceleration on the particle in the direction of its motion = g cos PTR = g PT ᎡᎢ = 9 AP 2 ᎡᎢ ( App . Art . 3 ) ...
Page 81
... circle . If the motion is very small , it will consist of small oscil- lations about the lowest point , which can be deduced from the case of the cycloid , the time of one of these complete oscillations ... CIRCLE . 81 Motion in a circle.
... circle . If the motion is very small , it will consist of small oscil- lations about the lowest point , which can be deduced from the case of the cycloid , the time of one of these complete oscillations ... CIRCLE . 81 Motion in a circle.
Page 82
... circle , R must never be positive ; if on the inside , or if suspended from O by a string , R must never be negative ; but if the particle be moving in a circular tube or groove , or be connected with O by a rigid rod , R may be either ...
... circle , R must never be positive ; if on the inside , or if suspended from O by a string , R must never be negative ; but if the particle be moving in a circular tube or groove , or be connected with O by a rigid rod , R may be either ...
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Common terms and phrases
accele acceleration produced axes axis balls center of force chord circle complete oscillation conic section constant acceleration cos² curve cycloid described determine the motion determined in Arts Differential Calculus direction of motion dt dt dt² earth's effect elastic ellipse equal equation fixed point focus force acting force of constraint force varying geometrical horizontal hyperbola impact impulse inclined plane inelastic initial direction initially at rest instant Ipswich School latus rectum Law of Motion length lowest point magnitude measure moving point NEWTON obtained Octavo orbit parabola parallelogram particle path perpendicular point of projection quantity of matter radius vector Second Edition Sermons shew sin² space passed straight line string supposed tangent tion Treatise Trinity College University of Cambridge v₁ versin vertex vis viva weight whence
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